Graziano Pelle's agent confirmed that the striker has been in talks with Everton, Stoke and an unnamed side from the Chinese Super League.
The 30-year-old has one year left on his current deal with the Saints, meaning he could leave for free next summer. Southampton are said to be offering the Italian forward a new deal, but if he is not willing to accept, then the Saints will be looking to cash in on his transfer this summer.
Southampton signed Pelle from Dutch side Feyenoord for a fee of £8m, with the target man going on to score 23 times in his 68 Premier League appearances.
Pelle's agent, Romualdo Corvino, has shed some light on his future, speaking to Italian radio station Sport Italia, he said, "With Juve at the moment there is nothing. However, there has been contact with Everton, Stoke City and China."
Pelle is out to impress in this summer's European Championships after being selected by head coach Antonio Conte. The Southampton forward is likely to be the starting striker for Italy in France.
Incoming Chelsea boss Conte gave Pelle his international debut and the striker has gone on to score five goals in thirteen appearances for the Azzurri.
If Pelle were to make the switch to Goodison Park he will be reuniting with incoming boss Ronald Koeman. The Dutch manager, who bought Pelle in, has been at St.Mary's for two years, and is expected to sign a £6m-a-year deal to manage Everton by the end of the week.
It is reported that Koeman will have £100m to spend on new players after Everton's new Iranian billionaire owner Farhad Moshiri reiterated his desire to see the Toffees in the Champions League.
Southampton, however, finished the season in sixth place, achieving Europa League football next season, whereas Everton finished in a disappointing eleventh.